Writing In The Math Class: A Different Approach To Ath Comprehension

READING AND WRITITNG ACROSS THE CURRICULUM: INCREASING MATHEMATICAL COMPREHENSION THROUGH THORUGH LITRACY LITERACY

Except where reference is made to the work of others, the work described in this thesis is my own or was done in collaboration with my Advisor. This thesis does not include proprietary or classified information.

Winnie Michelle Wood

Certificate of Approval:

Donald Livingston Associate Assistant Professor and Project Chair Education Title ii

A thesis submitted

Michelle Wood

Lagrange College

in partial fulfillment of the requirement for the degree of

Specialist in Curriculum and Instruction

LaGrange, Georgia Date December 22, 2010 Title iii

Abstract

The purpose of this study was to determine if writing in the math class made a difference in students’ achievement and affected students’ attitudes. The study consisted of three

Math 1 classes. The difference in mathematical achievement was analyzed using a t-test for independent means. The results indicated ______in achievement between classes where writing was implemented and those in which writing was not implemented.

The attitudinal effects were analyzed through students’ journal writings and reflections.

The students’ writings showed ______. The study suggests that the implementation of writing in math class ______. Title iv

CONTENTS

Abstract...... iii

CHAPTER ONE: INTRODUCTION...... 1

Statement of the Problem...... 1

Significance of the Problem...... 2

Theoretical and Conceptual Frameworks...... 7

Focus Questions...... 8

Overview of Methodology...... 10

Human as a Researcher...... 12

CHAPTER TWO: REVIEW OF THE LITERATURE...... 13

CHAPTER THREE: METHODOLOGY...... 23

Program Evaluation Research Design...... 23

Setting ...... 25

Sample / Subjects / Participants ...... 25

Procedures and Data Collection ...... 25

Validity, Reliability, Dependability, and Bias ...... 25

Analysis of Data...... 27

CHAPTER FOUR: RESULTS...... 28

CHAPTER FIVE: DISCUSSION OF RESULTS...... 30

Analysis...... 30

Discussion ...... 33

Implications ...... 33

Impact on Student Learning...... 33

Recommendations for Future Research...... 34

References...... 36 Title v

Appendix A ...... 39

Appendix B ...... 40

Appendix C ...... 41

Appendix D ...... 44

Appendix E ...... 45

Appendix F ...... 49

Appendix G...... 50

Appendix H ...... 51

Appendix I ...... 53 Writing in the Math Class 1

CHAPTER ONE: INTRODUCTION

Statement of the Problem

Social promotion – the practice of promoting a child to the next grade level regardless of his or her academic achievement – is an issue in today’s educational system that not only affects teachers and students but also society. The issue of whether to retain or promote a student whose performance is below grade level has been a subject disputed for years (Thompson, 2000), with strong advocates on both sides of the issue. President

Bill Clinton vowed to end social promotion in his State of the Union Address in 1999

(Department of Education, 1999), and then in 2002, President George W. Bush signed into law the education bill known as “No Child Left Behind” (Department of Education,

1999). Georgia’s law was amended by the A+ Education Reform Act of 2000, O.C.G.A.

§20-2-281, which requires that all students in grades one through eight take the Criterion

Referenced Competency Tests (CRCT). All students are tested in the content areas of reading, English/language arts and mathematics. Students in grades three through eight are also tested in science and social studies. The A+ Education Reform Act of 2000,

O.C.G.A. §20-2-281 also mandates that students in grades 9 through 12 take End of

Course Tests in core content areas (Georgia Department of Education, 2005). All too often, these standardized tests are used to decide the future of all Georgia students.

Those whose performance is “below grade level” are to be retained. While test-based grade promotion and retention is Writing in the Math Class 2

attractive, it is not supported scientificallysupported empirically. The curriculum was changed and standardized tests implemented, but those students who do not learn at a

“normal” pace are being left behind. The end result is that instead of no child being left behind, many more children are being left behind every year.

This issue is complex. Implementing a no-promotion policy may appear to be the right thing to do, but it cannot be replaced by simple retention (Thompson, 2000). This is where the problem lies. There are many issues that occur as a result of social promotion, as well as retention. When students are promoted without mastery in math, they are not prepared for the class into which they will be placed and are at an immediate disadvantage. Many do not even comprehend the basic operations: addition, subtraction, multiplication and division. All students can be successful if they are able to learn at their own pace. Not all students learn at the same pace, nor do they learn at the same level of proficiency or complexity (Fuentes, 1998). Unfortunately, since neither retention nor social promotion address a change in pace, neither is an effective means of increasing the performance of low-performing students.

Significance of the Problem

This research is not only important for students’ educational success, but also to mathematics teachers, as the implementation of the Georgia Performance Standards

(GPS) has arrived and now national standards now steadily approach. This study is an attempt to find a different approach to teaching mathematics, so that those students who Writing in the Math Class 3

are beginning their high school mathematics education, and are already behind, will truly comprehend the subject. The accelerated students will survive, but the students who are promoted without mastery or with weak skills need a different approach to help them find success in their mathematics class.

In a Northeast Tennessee High School, a study analyzed the relationship between social promotion and mathematics achievement as well as mathematics academic achievement and overall high school achievement among 30 seniors promoted without mastery. The results indicated a significant negative correlation between social promotion and high school mathematical achievement. There was also a strong positive correlation between mathematical achievement and overall high school achievement. In short, the study suggested that students socially promoted in middle school performed poorly in high school (Kariuki, 2001). Students who are socially promoted from middle school to high school are not prepared for the mathematics classes that our school system offers.

Currently, there are only two tracks available for our math students; Accelerated

Mathematics 1 and Mathematics 1 (see table 1.1). There is hHowever, there is a

Mathematics Support class for those students whothat qualify based on their eighth grade

CRCT test scores and middle school teacher recommendation. The purpose of the support class is to provide additional support to students so that they can meet the standards as well as preview material that they are going to learn in their Math 1 class. The goal is to help the students build a stronger foundation so that they will be successful in their Writing in the Math Class 4

current and future math classes (www.georgiastandards.org). Unfortunately, many students whothat would benefit from the class cannot take it because there are too few seats. On the other hand, there are students in the support classes whothat do not need to be in the class. As a system, for the time being, if these studentthey fail their Math 1 class then they also fail their Math Support class. Unfortunately, the curriculum is still taught at the same speed, and the support teacher is trying to differentiate for 15 to 21 (or more in some cases) students whose abilities are extremely diverse. The students will struggle through a class that they are not prepared for, or they will give up because it is too difficult. The material that they learned is quickly forgotten because they never had a true understanding of it. They have never had the chance to learn at their own pace and instead of losing one credit, they now lose two. Having taught a support class myself, I know how it is extremely difficult it is to support a group of students whose abilities differ so greatly. How can they understand if they were behind from the beginning? Yet, we don’tdo not worry about how to “fix” the problem. We keep moving through the curriculum, then give them a standardized test, a measure that determines their fate, to determine if they have learned the material. and decide their fate based on that standardized test.

Table 1.1 Math Tracks Writing in the Math Class 5

Table 1: Math Tracks

Mathematics Accelerated Mathematics

Mathematics I: Algebra/Geometry/Statistics Accelerated Math I: Geometry/Algebra II/Statistics Mathematics II: Geometry/Algebra II/Statistics Accelerated Math II: Mathematics III: Advanced Algebra/Geometry/Statistics Advanced Algebra/Statistics Mathematics IV: Accelerated Mathematics III: Pre-calculus-Trigonometry/Statistics Pre-calculus-Trigonometry/Statistics Other courses available: Discrete Mathematics AP Statistics Advanced Placement Calculus AB/BC Fourth year GPS courses Post-secondary options

It is not uncommon to find that some of the students never passed a mathematics

class in middle school. Often they do not know their basic math facts or the vocabulary

necessary to be successful. Even in the Math Support classes, the material is too difficult

for many of the students. In these cases, promoting them without mastery left them

unprepared and too far behind to begin a high school level class. Many times these

students cannot even write a mathematical statement such as 2 + 3 = 5. If they do not

understand a mathematical statement, how can they understand an algebraic equation, or

the characteristics of a parent function? Promoting them without mastery or at least some Writing in the Math Class 6

understanding of basic math facts leaves them with a low level of confidence and a feeling of helplessness. Those students who see themselves as helpless believe that there is nothing that they can do to be successful (Alderman, 1990). It is important for their future, as well as the future of educators, to help them find success.

The majority of the students lack the ability to communicate what they have learned; they are equally unable to communicate what they are having trouble understanding. This makes it very difficult to teach them the material they need to be successful in their math education. Because so many Sstudents are failing the state mandated End of Course Test, and as educators it is important that we, as educators, to find a way to help them succeed. The lack of understanding that exists before they reach high school makes it very difficult to teach them the material they need to be successful in their high school math education. With No Child Left Behind determining the fate of both teachers and students (Department of Education, 2002), it is important to find a way to help prepare students for what they will face in their high school career as well as life outside of high school. Promoting them without extra assistance designed to help them master the skills that are weak will hurt all stakeholders. If they are unable to communicate, how can they be successful after high school? When they are not successful after high school and do not become productive citizens, both the educational system and individual educators will – have failed them. The Georgia Performance

Standards states that students will learn to communicate mathematically (Georgia

Department of Education, 2005). According to The American Heritage Dictionary Need Writing in the Math Class 7

citation here, communication involves exchanging thoughts through speech, signals or writing. While it is an area in which mathematics teachers may not be proficient, promoting students without the communication skills will hinder them in their post-high school lives. For example, research indicates that 10 to 15 percent of high school graduates who did not pursue further education cannot balance their checkbook or write a letter to a credit card company to explain an error on their bill (Department of Education,

1999). Educators should be able to help those students who have weak communication skills instead of blaming the education system. Blaming the previous teacher or school for their lack of success does not help the students. Mathematics teachers should help students learn how to read, write, listen, speak and think math texts (Draper, 2002).

Theoretical and Conceptual Frameworks

This study researched methods of remediating mathematics that will truly help those students struggling to succeed. Socially promoting students is not effective, because they begin their classes already behind. One alternative to social promotion is retention, but there is an abundance of research that shows retention to have no lasting benefits for the student (Livingston & LivingstonD., 2002). In fact, when compared to promotion, those students retained typically showed lower levels of achievement and higher dropout rates (Hubert & Hauser, 1998/1999). Neither grade retention nor social promotion provides students with the support necessary to improve academic or social skills (Department of Education, 1999). The information resulting from this study will Writing in the Math Class 8

provide educators with a different approach to remediating math that will incorporate writing into the mathematics classroom, thus promoting comprehension and communication. It will provide educators with an alternative to the everyday drill and practice method of teaching mathematics, and will help increase mathematical comprehension, especially those students that are already behind and frustrated. Finding an alternative to helping “failing students” will lead to better educated citizens.

This study will focus on writing across the curriculum as a method of helping those struggling students to be successful in a math class. In the minds of most students and teachers writing occurs in language arts classes, not in mathematics classes. As secondary teachers, we worry about meeting deadlines and teaching the curriculum in our content area. We do not worry about other content areas until it affects our classes and even then we do not address the problem because it is not within our area of expertise.

The majority of mathematics teachers believe that teaching mathematics does not involve

“teaching writing.” Many mathematics teachers are of the mindset that they do not teach language arts and language arts teachers do not teach mathematics. Therefore, why shouldn’t the students expect mathematics to consist solely of numbers and “close their minds” when words are introduced? The fact is that there is more to mathematics than numbers and algorithms, but students that have weak literacy skills are going to struggle in all content areas. It is our job as educators to help these students attain the best education possible, no matter what subject area we teach. Writing in the Math Class 9

This research is based on Piaget’s and Vygotsky’s constructivist treatment of cognitive development. Constructivism is the belief that students create their own knowledge based on interactions with their environment and recognizes that a student’s experience and environment play a large role in how well the student learns. Piaget believed in active self-discovery, that students should be allowed to learn on their own by experimenting, posing questions and seeking the answers. Trying to teach students by simply talking to them does not increase their understanding (Brainerd, 1978). Vygotsky believed that learning takes place when the students interact with the social environment rather than in isolation (Daniels, 2001). As with all people, the life experiences of Piaget and Vygotsky influenced their beliefs. The two men communicated their ideas to one another when possible and often changed their views based on the views of the other.

Piaget and Vygotsky believed that it was the teacher’s responsibility to create an interactive learning environment. The teacher should guide the students in using their knowledge (Pass, 2004).

Students construct knowledge in different ways. Students who memorize facts or procedures without understanding are often unsure about when or how to use what they know. “When students understand mathematics, they are able to use their knowledge flexibly. They combine factual knowledge, procedural facility, and conceptual understanding in powerful ways” (National Council of Teachers of Mathematics, 2000).

Constructivism is enthusiastically expounded by the National Council of Teachers of

Mathematics (Carmen M. Latterell, 2005) and the National Council of Teachers of Writing in the Math Class 10

Mathematics guidelines were consulted while creating the newly implemented Georgia

Performance Standards (Georgia Department of Education, 2005). It would follow then, that constructivism should be useful in teaching mathematics in the classroom to help students gain meaningful and useful mathematical knowledge.

This study will incorporate writing into mathematics classes, and will focus on the work of Marilyn Burns as well as Warren E. Combs, Ph.D. as a guide for the students’ writing assignments. The goal in using writing in mathematics classes is to engage students in meaningful, real-life activities that encourage a higher level of thinking, even for the low performing students. The students’ writing will be used to guide them through their thought processes, and to clarify any misconceptions they may have.

This study is closely related to Tenet One of the Conceptual Framework, “an enthusiastic engagement in learning” (LCED, 2010). Under this, Competency Cluster 1.3 states that candidates must have the ability

This thesis also aligns to The National Council of Accreditation of Teacher

Education Standard One [NCATE] (2010)

There are Of the five core propositions that frame the foundation for national board certification established by the National Board for Professional Teaching Standards

(NBPTS), [NBPTS] (2010).t This study closely aligns with Proposition Number One; which states that “teachers are committed to students and their learning” (NBPTS, 2010). Writing in the Math Class 11

Focus Questions

The purpose of this study was to find a means of improving our students’ performance on the Georgia Mathematics 1 End of Course Test. There were three questions developed at the beginning of this study. First, does writing in math class increase achievement? Second, how do teachers and students feel about writing in the math class? Third, how successful is writing in the math class in reference to increased achievement as well as student and educator attitudes?

Overview of Methodology

This study was completed through action research. It was conducted at Troup

County Comprehensive High School in three Freshman Academy Math 1 classes. The students were required to keep math journals in which they reflected on the day’s activities and asked questions that they may have been uncomfortable asking in class.

Many of the students used the journal for taking notes as well as the reflections on the day’s lesson. In order to ensure confidentiality, pseudonyms are used throughout the study. .

The students in all classes were required to answer their essential at the end of each lesson. Additionally, rather than a typical final, their final was a writing assignment.

All Math I classes are required by the State of Georgia to take an End of Course Test, which is counted as their final. Instead of giving the Math I students another long Writing in the Math Class 12

multiple choice test, a math story about one of the topics covered in class during the semester was assigned ( see Appendix A).

As with any research, there were limitations that affected the results. A problem with all classes is attendance. Problems with attendance were a result of pregnancy, suspensions or dropping out. (Absences due to illness were not considered as a problem with attendance.) The students are allowed ?????? absences per semester without repercussions and after the ????, they must face the appeals board in an attempt to keep the credits possibly earned in classes in which they received a passing grade.

Another factor that needs to be considered is the fact that this class is the third class under the Math Georgia Performance Standards. The middle school teachers now have more experience teaching under the Georgia Performance Standards than they did the first year or even the second year. There has been a noticeable increase in the knowledge base in each group of rising ninth graders. There are, however, a few freshmen whothat do not have Math 1 or Math 1 Support. This year the county began a tTransitions class for those students whothat did not pass the Georgia CRCT.

It is also important to reveal that there were twenty-four students that I taught twice a day; once for Math 1 and once for Math 1 Support. Those students had more time writing mathematics than those whothat only took Math 1. Teaching mathematics through writing is easier said than done, but with practice and experience it becomes easier. Writing about math and writing math are not the same. The crucial step from writing from recollection to writing to learn is not easy (Zinsser, 19888). The goal is to Writing in the Math Class 13

assist all students in achieving a true understanding of the math topics that are discussed, not just to recall memorized math facts.

Human as a Researcher

As a high school mathematics teacher, I have had the pleasure of teaching students of all ability levels. There are many students whothat believe they cannot do math. We push them through a rigorous curriculum and some of them never get to master any of the content. This leaves them with a sense of helplessness. All students need to feel successful. I realize that not all students learn the same way, nor at the same rate. However, I do not believe that because of learning differences that students cannot learn to be successful in their mathematics classes. I want my students to feel successful and know that there is nothing wrong because they may not learn as quickly as some.

In evaluating students’ writings, I will be better able to discern their thought processes, which will help me in clarify misconceptions and find other methods of instruction leading my students to success. Their writings will also help them see their own thought processes. Our county motto is “It’s all about learning,” so I want to help my students learn. It is my belief that the benefit of this study is two-fold; it will help me to be a better teacher and help my students become successful in mathematics. Writing in the Math Class 14

CHAPTER TWO: REVIEW OF THE LITERATURE

Mathematical literacy in some countries is called numeracy (Pugalee, 1999). It affects a child’s comprehension of mathematics. While there are those that find mathematics fun and invigorating, there are others who find mathematics intimidating and frightening (Fuentes, 1998). Students who fear mathematics often enter a mathematics class with the belief that they cannot be successful. Many of those fearful students are inclined to dislike mathematics. They have not mastered the basic skills needed in mathematics, and also have weak literacy skills that affect their comprehension in all other classes, including their mathematics class.

Learning mathematics is like learning a new language (Fuentes, 1989).

Mathematics is a complex language that is used for communicating, problem solving, sports and many other areas of life. The “language of mathematics” involves numbers, symbols and words which can be “interrelated and interdependent and at other times disjointed and autonomous” (Adams, 2003 need page number). Words can represent symbols or numbers, depending on the problem. Mathematics also involves natural thought processes as well as language processes (Fuentes, 1989). Weaknesses in mathematical literacy frequently stem from the inability to focus on the mathematical symbols as students attempt to read (Adams, 2003). To comprehend mathematics, students have to be able to integrate their linguistic, cognitive and metacognitive skills

(Adams, 2003). Writing in the Math Class 15 Title 16

It is important to remember that not all students learn at the same pace. Some students do well with algorithm skills, but when faced with a word problem they have difficulty. If the problem involves only symbols and numbers, those who excel in algorithms have little difficulty determining the solution to the problem. If the problem is presented in words and sentences, then the students must be able to comprehend the language before they can apply the correct algorithm. For students to solve any mathematical problem, they must first be able to read. It would follow then, that in order to improve students’ mathematical literacy and ability, we must first help them improve their reading ability (Fuentes, 2003).

There are many factors that are related to reading mathematics. One factor is the terminology, or as the students say, “the words.” Terminology can be a difficult concept in any subject. In mathematics, the terminology may be special to mathematics, borrowed from ordinary language or familiar words that when used in a mathematical context will have a new and different meaning (Fuentes, 2003).

For communication to be clear and precise in mathematics, the student must comprehend the meanings of the terminology. There is a difference between knowing a definition of a term and understanding a term’s meaning. It may be easier for some students to begin with informal definitions, such as a drawing of a specific shape. For example, if you ask the students to define a square, they may not know how to describe it in words, but they may be able to draw a picture. Informal definitions are a good starting point and should be encouraged because these informal definitions lead students to construct their own understanding of the term. It is essential, though, that these students develop an understanding of the formal definitions. Returning to our square, its Title 17 definition can be complex, because it has many different properties. The students build on their knowledge of squares as they proceed through their mathematics classes.

Eventually, when asked to define a square, the need to draw one will no longer be necessary. The students will be able to define a square as a quadrilateral with four equal sides and four 90-degree angles. When reading mathematical text, being able to recognize and use the formal definitions of mathematics is a critical part of comprehension (Fuentes, 2003).

Another issue encountered when reading mathematics is the terminology that has more than one meaning. There are many words used in mathematics that we borrow from ordinary language. For example, in one mathematical context, “range” refers to the difference between the highest and lowest terms in a set of data, but to some students, it the stovetop where mom cooks dinner. It is important to know what meaning a student is using when reading a problem. Words used in ordinary language can easily confuse a student who is trying to comprehend a mathematical problem in which those words are used (Adams, 2003).

A third issue is homophones. Homophones are words that have the same pronunciation, but may have different spellings and different meanings. One example of homophones is the words one and won. They are pronounced the same but they have different meanings (Adams, 2003). Homophones could easily confuse a student and interfere with comprehension in a mathematical text. It is important for students to recognize and comprehend the differences between homophones.

A fourth issue is “sound-alike words,” or words that have similar sounds. The words are spelled differently, but have similar sounds. One example of words that are Title 18 sound-alike words is cents and sense. These two words have different meanings, but they sound similar to many people.

All four of these issues can interfere with students’ comprehension of what is being read (Adams, 2003). In order for a student to understand what a problem is asking, they have to know the meanings of the terminology.

Another area that can affect comprehension in mathematical text is symbols. It is imperative that students understand the meanings of the symbols so they may read mathematics effectively (Adams, 2003). Because Ssymbols are not uncommon in mathematics, and students need to be able to decipher them when they are reading mathematics. Dollar signs are not the only types of symbols used in mathematics. In fact, most symbols are used to tell the student what operation to use. Symbols also provide mathematics with organization and management, specifically the order of operations. It is imperative that students understand the meanings of the symbols so they may read mathematics effectively (Adams, 2003). The use of an incorrect symbol will completely change the answer. Students should be able to translate words to symbols and symbols to words (Adams, 2003).

Terminology is only one aspect that affects mathematical literacy. Students also need to be able to read numbers in context to fully comprehend the language of mathematics. The meaning of numbers can change depending on whether symbols are used or not used. For example, “777-335-2150” is a telephone number. The meanings may not always be obvious, but it is important that students be familiar with the formats of numbers that may be embedded in the text. Students also need to be familiar with abbreviations and symbols that they will see when reading mathematical text. For Title 19 example, “16 lb.” represents 16 pounds. Another example is the dollar sign (Adams,

2003).

As educators, we should be aware of the problems that can occur relating to terminology, symbol recognition and reading in context so that we can help strengthen students’ mathematical literacy skills. We can use many different strategies to help improve students’ understanding of mathematical terminology and recognizing symbols.

Word walls can be developed using terminology and symbols. A student-made mathematical dictionary can be created by using terminology as well as symbols.

Graphic organizers are also effective in increasing mathematical literacy. We can also use games, such as Bingo, Memory, Jeopardy and many more. All of these strategies are fairly simple and even fun for the students, but they do not require higher-order of thinking.

One effective strategy that requires students to use a higher-order of thinking is a math journal (Romberg, 1992). Of course, students and many mathematics teachers feel that journals, as well as any other types of writing, do not belong in a mathematics class.

A math journal is an excellent way to introduce writing into a mathematics class (Burns,

2001). Writing is a large part of literacy, and if students can write about mathematics, then their mathematical literacy is improving. The writing process requires gathering, organizing and clarifying thoughts. It requires finding out what you know and do not know. Mathematics also requires gathering, organizing and clarifying thoughts as well as finding out what you know and do not know. Writing and mathematics both require clear thinking. The students’ mental journey is essentially the same: making sense of an idea and presenting it successfully (Burns, 1995). Having students write in journals helps Title 20 them to express themselves and keep track of their reasoning. “Writing is a way to work yourself into a subject and make it your own” (Zinsser, 1988, p. 16). Writing can assist mathematics in two ways: it helps students make sense of mathematics and it helps teachers understand what students learned (Burns, 1995). As educators, we can evaluate students’ progress and identify their strengths as well as their weaknesses (Burns &

Silbey, 2001). Journal writing is one tool that can assist teachers in doing just this.

Journal writing prompts can be used to see how students perceive homophonic or sound- alike words (Adams, 2003). Journal writing can also be used to keep notes and work problems, or when creating their own mathematical dictionary. Journal writing can also be used as a useful reflective tool. Joan Countryman need citation sometimes allows her students to use their journals to clear their heads. Most students come into class with other issues on their minds that they need to express. Writing what is on their minds in their journals for the first ten minutes of class makes the students more available for learning and participating in class (Zinsser, 19888).

Writing a journal entry does not necessarily come naturally, therefore must be taught. Helping students become comfortable with writing in mathematics class takes time and effort. The first attempts are often difficult for students as well as discouraging for teachers. It takes a great deal of encouragement and practice (Burns, 1995). Upper level teachers can use prompts such as:

1. What I know about ____ so far is ____.

2. What I’m still not sure about is ____.

3. What I’d like to know more about is ____ (Burnsneed page number, 2001). Title 21

When using a journal for writing in math class, students often find mathematics more meaningful (Romberg, Thomas 1992).

One of the greatest problems with math journals is that evaluating them is extremely time-consuming. However, it is unnecessary to give individual comments on each entry; individual feedback is most useful when assessing individual progress. It is important to read for clarity and completeness. When giving individual feedback, we should avoid comments that don’tdo not give students authentic feedback. Feedback should be encouraging, honest and specific (Burns, 1995). It is also beneficial to students to show an interest in how they think and offer suggestions that will further their cognitive skills (Burns, 2001).

Laurie Pines (2003), a high school math teacher, uses stories as a learning tool to help improve mathematical literacy and comprehension. A graphic organizer is one activity that can be used with stories to improve reading comprehension as well as writing skills. Pines uses a two-column graphic organizer to help students become aware of their own metacognitive processes. The graphic organizer helps students become aware of “the conversation in their heads” as they are reading. If they are aware of “the conversation in their heads,” then it becomes easier for them to write (Pines, 2003).

To use the two-column graphic organizer, students record thought-provoking words from the text in the left-hand column. Next, in the right-hand column, they write their own thoughts or questions that were triggered by the text in the left-hand column.

Students can record their two-column graphic organizer in their math journals. Pine uses

Stories to Solve by George Shannon to introduce students to this particular graphic organizer. More Stories to Solve and Still More Stories to Solve, both by George Title 22

Shannon, can also be used with this particular graphic organizer. The stories in all three of these books require deductive reasoning, which is an essential skill in mathematics

(Pines, 2003).

Students benefit when literature is used to illustrate mathematics. The illustrations help students visualize the problem at hand and encourage them to use pictures to help with their own problem solving. Their writing may include numbers, words and pictures (Burns, 1995). Often students, – especially in high school, – forget to use pictures to assist in their problem-solving strategies. An abundance of materials exists for the elementary level, but there are far fewer resources for the middle grades and even fewer for the high school level. That does not mean that the books from the elementary level cannot be used on the high school level. While the students may find them silly at first, these lower level materials still help them to develop their deductive reasoning skills. The books from the elementary level contain pictures which are very often extremely helpful in mathematics. Introducing literature into mathematics classes helps students build their mathematical literacy skills and improve their deductive reasoning skills. Improving mathematical literacy and deductive reasoning skills helps prepare students to successfully read and evaluate word problems need a citation here.

Reading word problems is different from reading stories or pages from textbooks

(Fuentes, 1989). Many students refuse to attempt word problems because of literacy and reading comprehension issues. Reading word problems involves recognizing concepts and relationships that are not obvious, but may be implied or assumed. Students not reading at grade level and students whose first language is not English are at a Title 23 disadvantage (Fuentes, 1989). Word problems create a feeling of anxiety for many students, not just those students with weak literacy skills.

There are many different methods used to teach students to solve word problems.

There is no single successful tactic, and it is important to remember that not all students learn at the same pace or at the same level of complexity or proficiency (Fuentes, 1998).

It is important that students possess decoding skills so they can determine which information is relevant to answering the question and which information extraneous.

They must also be able to translate words to symbols. Giving students the opportunity to read word problems and examine the information given, or omitted, helps them to develop their skills for solving word problems. George Polya (as cited in Adams, 2003), referred to as the “father of problem solving,” is known for his four-step problem solving process:

1. Read the problem.

2. Understand the problem.

3. Solve the problem.

4. Look back (Adams, 2003 need page number).

Most problem solving processes revolve around these four steps.

Mathematical literature and “story problems” are two more methods of increasing mathematical literacy. “Story problems” are also good for journal entries. Arithme-tickl, by J. Patrick Lewis (need a citation here) is a book of “riddle-rhymes” that encourages deductive reasoning and can be used as a journal entry. Riddles are shorter than stories and which can be less intimidating. Mathematical literature, “story problems” and riddles can help prepare students for the task of solving word problems. A math journal can be Title 24 an effective tool to use when attempting to conquer word problems. Because math journals help students organize their thoughts, they are a useful tool in decreasing the anxiety students feel when faced with a word problem. Modeling how to approach a word problem can also help decrease anxiety. The more knowledge students have about mathematics, the better they will be able to comprehend mathematical text (Fuentes,

1998). Too often students learn and practice procedures without understanding why they work (Burns, 1995).

Word problems involve the interaction between words, numbers and symbols.

This three-way relationship often has the mathematical message embedded within it.

Adams (2003) phrases it: Words tell. Numbers listen. Symbols show. The words tell the reader what is to be known and what is to be done. The numbers are guided by what the words tell and symbols show us how to respond to the numbers. If the students do not comprehend the words, or what the numbers and symbols represent, then their chances of success are small. Writing to solve word problems gives students as well as teachers a record of the students’ thinking process as they solve the problem (Burns, 1995). Title 25

CHAPTER THREE: METHODOLOGY

Program Evaluation and Research Design

This research is both a quantitative and qualitative study. It was conducted with the intent of providing mathematics teachers – particularly secondary level teachers – with useful information, ideas and methods concerning reading and writing in the classroom. LteracyLiteracy is important in all content areas of education. As professional educators, mathematics teachers should be less resistant to combining literacy instruction with the “regular teaching of mathematics” (Draper, 2002).

The quantitative component of the research will compare statistics from benchmark tests and End of Course Tests. The difference in achievement of two groups of Math 1 students is analyzed using an independent t-test of benchmark test results as well as End of Course Tests results. The qualitative component of the research is based on common themes and changes in attitude displayed in students’ writing.

Setting

The study took place at Troup County Comprehensive High School in Troup

County Georgia (wording). The study was approved by the principal as well as the local board of education.

Sample / Subjects / Participants

The participants consisted of students in two independent groups of Math 1 students. The students were grouped heterogeneously based on their eighth grade CRCT Title 26

scores. Math 1 is the first high school mathematics class for those students who score at

or below 849 on the mathematics section of the eighth grade CRCT.

Procedures and Data Collection Methods

Table 3.1 Data Shell Focus Literature Type of Why these How these Rationale Strengths/ Question Sources Method and data provide data are Weaknesses Data valid data analyzed

Does writing Zinsser, Method: Type of Quantitative: Quantitative: Validity in math class 1988 Midterms, Validity: Descriptive Determine if Reliability increase Draper, EOCT Content and there are Dependability student test 2002, Inferential significant scores? Adams, Data: Statistics differences 2003 Quantitative independent in test scores and dependent t-tests using paired data

How do Burns, 1995 Method: Type of Quantitative: Qualitative: Strengths: teachers and Romberg, Surveys, Validity: Likert Look for Validity students feel 1992 Journals Construct Surveys categorical Reliability about Chi Square and Dependability writing in Data: Test repeating the math Qualitative data Weakness: class? Qualitative: Bias Coded for Themes Reflections Title 27

How Burns, Method: Type of Quantitative: Quantitative: Strengths: successful 2001 Reflection Validity: Independent Determine if Validity was writing Romberg, Predictive t-tests there are Reliability in the math 1992 Data: Chi-Square significant Dependability class in Pines, 2003 Interval Effect Size differences reference to Qualitative: increased Qualitative: Look for achievement Coded for categorical as well as Themes and student and Reflection repeating educator data attitudes?

Validity, Reliability, Dependability, and Bias

Analysis of Data Title 28

CHAPTER FOUR: RESULTS Title 29

CHAPTER FIVE: ANALYSIS AND DISCUSSION OF RESULTS

Analysis

Discussion Implications

Impact on Student Learning

Recommendations for Future Research Title 30

References

Alderman, K. (1990). Motivation for at-risk students. Educational Leadership, 48(1).

Retrieved June 20, 2010, from Ebsco Host Web site:

http://web.ebscohost.com.relay.lagrange.edu/ehost/pdfviewer/pdfviewer?

vid=8&hid=105&sid=7dabce34-5ffa-495a-b515-7f76a064a5ee

%40sessionmgr114

Brainerd, C. (1978). Piaget's theory of intelligence. Englewood Cliffs, NJ: Prentice-Hall,

Carmen M. Latterell. (2005). Math wars: A guide for parents and teachers. Westport,

Connecticut: Praeger Publishers.

Daniels, H. (2001). Vygotsky and pedagogy [Electronic version]. New York: Routledge

Falmer.

Department of Education. (1999). Executive Summary [Taking responsibility for ending

social promotion: A guide for educators and state and local leaders]. Available

from Department of Education,

http://www2.ed.gov/pubs/socialpromotion/directive.html

Department of Education. (2002). No Child Left Behind [NCLB Overview]. Available

from Department of Education, http//:www.ed.gov/nclb

Eisner, Caroline. (Ed.). (2000). Ending social promotion: Early lessons learned in the

efforts to end social promotion in the nation's public schools (Office of

Elementary and Secondary Education (ED), Washington, DC) [Electronic

version]. Washington, U.S: Council of the Great City Schools, Washington, DC. Title 31

Fuentes, P.eter. (1998). Reading comprehension in mathematics. Clearing House, 72(2),

81-88.

Georgia Department of Education. (2005). Office of Curriculum and Testing [Testing].

Available from Georgia Department of Education, http://public.doe.k12.ga.us

Georgia Department of Education. (2005). One Stop Shop for Educators [Georgia

Performance Standards]. Available from Georgia Department of Education,

www.georgiastandards.org

Greenberg, D. (2002). 200 Super-fun, super-fast math story problems. New York:

Scholastic Inc.

Hubert, R., & Hauser, R. (Eds.). (1999). High stakes: Testing for tracking, promotion,

and graduation [Electronic version]. Washington, D.C: National Academy Press.

(Original work published 1998)

Kariuki, P.atrick. (2001). The Relationship between social promotion in the middle

school and academic achievement in a high school math class [Electronic

version]. Tennessee, United States: Science, Mathematics, and Environmental

Education. (ERIC Document Reproduction Service No. ED464839)

Livingston D., & Livingston, S. (2002). Failing Georgia: The case against the ban on

social promotion. Education Policy Analysis Archives, 10(49). Retrieved June 14,

2005, from http://epaa.asu.edu/epaa/v10n49/

National Council of Teachers or Mathematics. (2000). Overview: Principle for School

Mathematics [The Learning Principle]. Available from NCTM, http://

standards.nctm.org Title 32

Pass, S. (2004). Parallel paths to constructivism: Jean Piaget and Lev Vygotsky.

Greenwich, Connecticut: Information Age Publishing, Inc.

Romberg, T. (Ed.). (1992). Mathematics Assessment and Evaluation: Imperatives for

Mathematics Educators. Albany: State University of New York Press.

Thompson. Need initial (2000). Retention and social promotion: Research and

implications for policy [Electronic version] (Report No. EDO-UD-00-0). New

York: ERIC Clearinghouse on Urban Education, New York, NY. (ERIC

Document Reproduction Service No. ED449241) Title 33

Appendix A Title 34 title 35